When you mention drag-and-drop do you mean to the main Calibre window? On other OS this acts like an "Add Books" so if it does not on OSX I would have thought this needs looking at. However if you mean directly to the underlying file system then this outside of Calibre's remit.
I do not think you should be expecting the browsers to understand the OPDS feed. The format of an OPDS feed is not one that browsers will normally be aware of. If you have any that work I would have thought that was just by accident as the OPDS standard is based on the Atom standard which some browsers understand.
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